INSTRUCTIONS
 This paper consists of two sections 1 and 2. Answer all the questions in section 1 and any 5 questions in section 2.
 KNEC mathematical tables and electronic non programmable calculators may be used where necessary.
SECTION 1
Answer all questions in this section
 Find without using tables or a calculator the value of (3mks)
1.33 ×0.51
0.19 ×0.0017  The ratio of the size of the exterior angle to the interior angle of a regular polygon is 1:3. Determine the number of sides of the polygon and name it. (3mk)
 Given that 2x^{2}−kx+18 is a perfect square, find k and hence solve the equation 2x^{2}−kx+18=0 by factorization. (4mk)
 Work out using logarithms to 4 s.f (4mk)
√ (6.225log1.001)
(56.7×0.031)^{3}  Mr. Kanja,Miss Kanene and Mrs Nyaga have to mark a form three math contest for 160 students. They take 5mins, 4mins, and 12mins respectively to mark a script. If they all start to mark at 9.00 am nonstop, what is the shortest time they can take to complete the marking? (3mk)
 Jackie takes 5minutes to run a distance of 1km in a race. Express her speed in (2mk)
 km/hr
 m/s
 Use reciprocal tables to find the value of f given that ^{1}/_{f }= ^{1}/_{11 }+ ^{2}/_{13} (3mk)
 A man left ^{1}/_{5 }of his estate in Kerugoya to his wife and ^{1}/_{3} to each of his two sons .The remainder was to be shared equally among his six brothers. If the estate was worth sh 3 456 000, how much did each of those people get? (3mk)
 A distance of 12km is represented by a length of 4cm on a map. Given that the scale of the map is 1:n, find the
 value of n
 actual area in hectares of a field on the map with an area of 32cm^{2}(3mk)
 Solve the equation ^{1}/_{3}(x+4) − ½(2x–4) =2 (2mk)
 The sides of a right angled triangle measured to the nearest cm are 5cm, 12cm and 13cm
Determine the limits within which the measured dimensions lie (1mk)
 percentage error in the area of the triangle. (3mk)
 Form a quadratic equation in the form ax^{2}+bx+c=0 whose roots are b and twice the negative reciprocal of b. (3mk)
 The coordinates of points A and B are A (2, 3).B (4,–5). M is the midpoint of vector AB.
Determine the coordinates of point M and the magnitude of vector BM. (3mk)  The equation of line L is y=3x–4 and is perpendicular to line H. They cross each other at the yintercept of line L. Find the equation of line H. (3mk)
 In a circle radius 10cm, an arc PQ subtends an angle of ^{5}/_{12}π radians at the centre of the circle. Calculate the radius of another circle whose circumference is equal to the length of arc PQ (4mk)
 Solve for a in 3^{2a+3}=2187 (3mk)
SECTION 2
Answer any 5 questions in this section
 Four towns are situated in such a way that town Q is 500km on a bearing of 120º from P. Town R is 240km on a bearing of 210º from town P, while town S is due north of town Q and due east of town P.
 Draw a sketch diagram showing the relative positions of P, Q, R and S. (2mk)
 Find by calculation
 the distance QR (2mk)
 the distance QS (2mk)
 the angle PRQ (2mk)
 area of triangle PQS (2mk)

 Represent the following inequalities graphically by shading the unwanted region
x≥0, y≥0, x+y≥5, x+y≤10, y≤7, x≤7 (6mks)  write down the coordinates of one point that is inside the wanted region (1mk)
 Name the figure formed by the unshaded region (1mk)
 measure and find the sum of all the angles in the figure formed in (c) above. (2mk)
 Represent the following inequalities graphically by shading the unwanted region
 In the figure below, O is the centre of the circle and ∟EAD=40º,∟BCD=118º
Find giving reasons ∟ADE (2mk)
 reflex ∟EOD (2mk)
 ∟EBD (2mk)
 ∟EAB (2mk)
 ∟DAB (2mk)
 The marks scored in a form three maths exam were recorded as follows
69 70 72 40 52 60 22 31 78 53 28 67 63 54 57 48 47 56 55 62
75 38 37 44 62 64 58 39 45 48 65 50 85 46 47 57 35 34 58 64
62 37 41 42 36 54 82 48 53 57 56 72 56 48 44 55 78 59 50 45 Make a grouped frequency table with classes 20—29,30—39,40—49,etc (2mk)
 What is the modal distribution of the test (1mk)
 Calculate the mean of the data (4mk)
 Calculate the median mark (3mk)
 The velocity(v)of a vehicle measured at intervals of time(t) were recorded as follows
t(s) 0 2 4 6 8 10 12 v(m/s) 0 20 40 40 30 8 0  Represent this motion on a graph (3mk)
 Calculate the acceleration (2mk)
 Calculate the total distance travelled by the vehicle (3mk)
 Calculate the average velocity of the vehicle (2mk)
 A wooden stool is in the form of a frustum of a cone with slant edge 40cm,top diameter 30cm and bottom diameter 50cm.
 calculate the perpendicular height of the stool (3mk)
 calculate the total surface area of the stool in terms of π (3mk)
 calculate the volume of wood used to make the stool in terms of (3mk)
 given that the density of the wood used to make the stool is 0.8g/cm³, calculate the mass of the stool in kg (1mk)
 Using ruler and compasses only,
 construct triangle ABC in which AB=5cm,BC=6cm and angle ABC=120º. (3mk)
 measure angle ACB (1mk)
 drop a perpendicular from C to cut AB produced at P. Measure CP. (2mk)
 hence calculate area of triangle ABC to 1dp (2mk)
 calculate the radius of a circle that passes through the vertices of triangle ABC (2mk)
 The distance between two towns A and B is360km.A minibus left town A at 8.15a.m and travelled towards B at an average speed of 90km/hr. A matatu left town B at 10.35a.m on the same day and travelled towards A at an average speed of 110km/hr.

 how far from A did they meet? (4mk)
 at what time did the two vehicles meet? (2mk)
 A motorist left his home at 10.30a.m on the same day and travelled at an average speed of 100km/hr. He arrived at B at the same time as minibus. Calculate the distance from B to his home. (4mk)

Marking Scheme
 Find without using tables or a calculator the value of (3mks)
1.33 ×0.51 × 1000000
0.19 ×0.0017 1000000
= 133 × 51 × 100
19 × 17
=2100  The ratio of the size of the exterior angle to the interior angle of a regular polygon is 1:3. Determine the number of sides of the polygon and name it. (3mk)
Ext:Int
1: 3
1 ext =¼ × 180 =45°
No. of sides = 360 =8 sides
45
NameOctagon  Given that 2x^{2}−kx+18 is a perfect square, find k and hence solve the equation 2x^{2}−kx+18=0 by factorization. (4mk)
(−k)^{2} = 2 × 18
( 2 )
K^{2} =36 × 4
=144
K=±12
2x^{2} − 12x + 18 = 0
2x^{2} − 4x − 9x + 18 = 0
2x(x−2) −9(x−2) = 0
(x−2) (2x−9) = 0
x = 2
x=4½  Work out using logarithms to 4 s.f (4mk)
√ (6.225log1.001)
(56.7×0.031)^{3}
10^{−3} × 9.592 = 0.009592  Mr. Kanja,Miss Kanene and Mrs Nyaga have to mark a form three math contest for 160 students. They take 5mins, 4mins, and 12mins respectively to mark a script. If they all start to mark at 9.00 am nonstop, what is the shortest time they can take to complete the marking? (3mk)
LCM of 5, 4, 12 =60 M1
In 60 mins Kanja 12 scripts
Kanene 15 scripts
Nyaga  5 scripts
All 32 scripts M1
60 → 32
? → 160
=300mins =5hrs A1  Jackie takes 5minutes to run a distance of 1km in a race. Express her speed in (2mk)
 km/hr
1km =1 × 60 = 12km/hr B1
^{ }^{5}/_{60} 5  m/s
1000m = 3^{1}/_{3}m/s B1
5×60
 km/hr
 Use reciprocal tables to find the value of f given that ^{1}/_{f }= ^{1}/_{11 }+ ^{2}/_{13} (3mk)
1.1×10^{−1} =0.9091 × ^{1}/_{10} =0.09091×1= 0.0909
1.3×10^{−1} =0.7692 × ^{1}/_{10} =0.07692×2=+ 0.1538
^{1}/_{f} = 0.2447
2.447 × 10^{−1} =0.4086 × 10^{−1}
f=4.086  A man left ^{1}/_{5 }of his estate in Kerugoya to his wife and ^{1}/_{3} to each of his two sons .The remainder was to be shared equally among his six brothers. If the estate was worth sh 3 456 000, how much did each of those people get? (3mk)
^{1}/_{5} + ^{1}/_{3} + ^{1}/_{3} = ^{13}/_{15}
Brothers = ^{2}/_{15}Wife = ^{1}/_{5} × 3456000 = sh.691,200
Each son = ^{1}/_{3} =3456000 = sh.1,152,000
Each brother = Remainder = 460800 = sh.76800
6 6  A distance of 12km is represented by a length of 4cm on a map. Given that the scale of the map is 1:n, find the
 value of n
4 cm : 12 km
4 cm : 12000 m
4 cm : 1200000 cm
=1 : 300,000  actual area in hectares of a field on the map with an area of 32cm^{2}(3mk)
1 cm : 3,000 m
1 cm^{2} : 9,000,000 m^{2}
32 cm^{2} : 288,000,000 m^{2}
we know 1 hectare = 100 m by 100 m or 10,000 m^{2}
so 288,000,000 m^{2} = 288,000,000
10,000
=28,800 hectares
 value of n
 Solve the equation ^{1}/_{3}(x+4) − ½(2x–4) =2 (2mk)
^{1}/_{3}x + ^{4}/_{3} − x +2 =2 M1
−^{2}/_{3}x = ^{−4}/_{3}
x = ^{−4}/_{3} × ^{−3}/_{2}
=2 A1  The sides of a right angled triangle measured to the nearest cm are 5cm, 12cm and 13cm
Determine the limits within which the measured dimensions lie (1mk)
Upper limits Lower limits
5.5 4.5
12.5 11.5
13.5 12.5 B1  percentage error in the area of the triangle. (3mk)
Actual area = ½ × 5 × 12 =30cm^{2}
Max area = ½ × 5.5 × 12.5 =34.375
Min area =½ × 4.5 × 11.5 =25.875 M1
% error = 34.375 − 25.875 × 100 M1
2
30
=14.17% A1
 limits within which the measured dimensions lie (1mk)
 Form a quadratic equation in the form ax^{2}+bx+c=0 whose roots are b and twice the negative reciprocal of b. (3mk)
x=b x=−^{1}/_{b} M1
(x−b)(x + ^{1}/_{b}) =0
x^{2} + ^{x}/_{b} − bx − 1=0 M1
x^{2} + (^{1}/_{b} − b)x −1 =0 A1  The coordinates of points A and B are A (2, 3).B (4,–5). M is the midpoint of vector AB.
Determine the coordinates of point M and the magnitude of vector BM. (3mk)
lBMl = √(−1^{2} + 4^{2}) =√17  The equation of line L is y=3x–4 and is perpendicular to line H. They cross each other at the yintercept of line L. Find the equation of line H. (3mk)
Grad of L =3
Grad of H =−^{1}/_{3} B1
Coors of intersection (0,−4)
y−−4 =−^{1}/_{3}
x
3(y=4)=−x M1
3y+12=−x
3y=−x−12 A1  In a circle radius 10cm, an arc PQ subtends an angle of ^{5}/_{12}π radians at the centre of the circle. Calculate the radius of another circle whose circumference is equal to the length of arc PQ (4mk)
Length of Arc PQ = M1
=^{25}/_{2}π A1
^{25}/_{2}π= 2πr ∴ r = ^{25}/_{2}π × ^{1}/_{2π} M1
=^{25}/_{4} =6.25cm A1  Solve for a in 3^{2a+3}=2187 (3mk)
3^{2a+3} = 3^{7} M1
2a+3=7 M1
2a=4
a=2 A1
SECTION 2
Answer any 5 questions in this section
 Four towns are situated in such a way that town Q is 500km on a bearing of 120º from P. Town R is 240km on a bearing of 210º from town P, while town S is due north of town Q and due east of town P.
 Draw a sketch diagram showing the relative positions of P, Q, R and S. (2mk)
 Find by calculation
 the distance QR (2mk)
QR=√(500^{2} + 240^{2})
=554.7km  the distance QS (2mk)
Sin 30 = QS
500
QS =500 sin 30
=250km  the angle PRQ (2mk)
Tan PRQ =500 =2.083
240
∟PRQ =64.36°  area of triangle PQS (2mk)
A = ½ × 500 × 250 sin 60
= 54126.6km^{2}
 the distance QR (2mk)
 Draw a sketch diagram showing the relative positions of P, Q, R and S. (2mk)

 Represent the following inequalities graphically by shading the unwanted region
x≥0, y≥0, x+y≥5, x+y≤10, y≤7, x≤7 (6mks)
x+y≥5x 0 5 y 5 0 x 0 10 y 10 0  write down the coordinates of one point that is inside the wanted region (1mk)
Any one  Name the figure formed by the unshaded region (1mk)
 Hexagon
 measure and find the sum of all the angles in the figure formed in (c) above. (2mk)
135° × 4
90° × 2
sum =720°
 Represent the following inequalities graphically by shading the unwanted region
 In the figure below, O is the centre of the circle and ∟EAD=40º,∟BCD=118º
Find giving reasons ∟ADE (2mk)
∟ADE = 50°
(∟AED =90°− Ls in a semicircle)  reflex ∟EOD (2mk)
reflex ∟EOD =360 − (40×2)
=360 −80 =280°
(∟ at centre =2∟ on circumference)  ∟EBD (2mk)
∟EBD=40°
(∟s in same segment)
(or ∟s subtended by the same chord/arc)  ∟EAB (2mk)
∟EAB=90°
(∟s in a semicircle)  ∟DAB (2mk)
∟DAB =180 − 118 = 62°
(Opp. ∟s in a cyclic quad are supp.)
 ∟ADE (2mk)
 The marks scored in a form three maths exam were recorded as follows
69 70 72 40 52 60 22 31 78 53 28 67 63 54 57 48 47 56 55 62
75 38 37 44 62 64 58 39 45 48 65 50 85 46 47 57 35 34 58 64
62 37 41 42 36 54 82 48 53 57 56 72 56 48 44 55 78 59 50 45 Make a grouped frequency table with classes 20—29,30—39,40—49,etc (2mk)
Class f x xf c.f 2029
3039
4049
5059
6069
7079
80892
8
14
18
10
6
2
6024.5
34.5
44.5
54.5
64.5
74.5
84.549
276
623
981
645
447
169
31902
10
24
42
52
58
60  What is the modal distribution of the test (1mk)
 5059 B1
 Calculate the mean of the data (4mk)
x̄ =3190 = 53.17 M1
60 A1  Calculate the median mark (3mk)
M=49.5 + (30 − 24) × 10 M1
18
=49.5 + ^{10}/_{3} = 52.83 A1
 Make a grouped frequency table with classes 20—29,30—39,40—49,etc (2mk)
 The velocity(v)of a vehicle measured at intervals of time(t) were recorded as follows
t(s) 0 2 4 6 8 10 12 v(m/s) 0 20 40 40 30 8 0  Represent this motion on a graph (3mk)
 Calculate the acceleration (2mk)
Acc = 40 − 0 M1
4 −0
=10m/s A1  Calculate the total distance travelled by the vehicle (3mk)
Area of A =½ × 4 × 40 = 80
B = 40 × 2 = 80
C = ½(40+30)2 =70
D =½(30+8) 2 =38
E =½ × 2× 8 = 8 M1M1
Total 276 A1  Calculate the average velocity of the vehicle (2mk)
Av. velocity = 276 =23m/s M1 A1
12
 Represent this motion on a graph (3mk)
 A wooden stool is in the form of a frustum of a cone with slant edge 40cm,top diameter 30cm and bottom diameter 50cm.
 calculate the perpendicular height of the stool (3mk)
15 = L
25 L+40
15L + 600 = 25L
L=60cm
H=√(100^{2} − 25^{2}) =96.82cm
96.82 =100
h 60
h = 58.09cm
Perpendicular height = 96.82−58.09
= 38.73  calculate the total surface area of the stool in terms of π (3mk)
Base = πr^{2} =625π
Top = =225π
C.S.A=πRL − πrl
=2500π − 900π = 1600π
T.S.A = 2450π  calculate the volume of wood used to make the stool in terms of (3mk)
v=^{1}/_{3} × 625π × 96.82 − ^{1}/_{3} × 225π × 58.09
=20170.8π − 4356.75π = 15814.05π  given that the density of the wood used to make the stool is 0.8g/cm³, calculate the mass of the stool in kg (1mk)
M=v × d
= 15814.05 × 3.143 × 0.8
1000
=39.76kg
 calculate the perpendicular height of the stool (3mk)
 Using ruler and compasses only,
 construct triangle ABC in which AB=5cm,BC=6cm and angle ABC=120º. (3mk)
 measure angle ACB (1mk)
∟ ACB =27° ±1°  drop a perpendicular from C to cut AB produced at P. Measure CP. (2mk)
CP=5.2cm ±0.1cm  hence calculate area of triangle ABC to 1dp (2mk)
A=½ × 5 × 5.2 = 13cm^{2}  calculate the radius of a circle that passes through the vertices of triangle ABC (2mk)
5 = 2r
sin 27
∴ r = 5 = 5.507
2sin 27
 construct triangle ABC in which AB=5cm,BC=6cm and angle ABC=120º. (3mk)
 The distance between two towns A and B is360km.A minibus left town A at 8.15a.m and travelled towards B at an average speed of 90km/hr. A matatu left town B at 10.35a.m on the same day and travelled towards A at an average speed of 110km/hr.

 how far from A did they meet? (4mk)
Distance travelled by minibus when matatu leaves B
90 × 2^{1}/_{3} = 90 × ^{7}/_{3} =210km
R.d = 360 − 210 =150
R.s = 90 + 110 = 200
t = 150 ×60 =45mins
200
Distance minibus has travelles = 90 × 3^{5}/_{60}
=90 × 185 =277.5km
60  at what time did the two vehicles meet? (2mk)
10.35
+ .45
11.20
=11:20am
 how far from A did they meet? (4mk)
 A motorist left his home at 10.30a.m on the same day and travelled at an average speed of 100km/hr. He arrived at B at the same time as minibus. Calculate the distance from B to his home. (4mk)
Time minibus reached B
360 = 4hrs
90
8.15 + 4 = 12.15pm
Time motorist took = 12.15
−10.30
1.45
=1hr 45mins
d= 100 × 1^{45}/_{60}
^{ }=100 × 1^{3}/_{4}
=100 × ^{7}/_{4} =175km

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